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A113875
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Slowest growing sequence of primes having the prime-pairwise-average property: if i<j, (a(i)+a(j))/2 is prime.
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5
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3, 7, 19, 139, 859, 8179, 173059, 1026199, 1827139, 15828679, 13187242759, 18732483199, 912492556939
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OFFSET
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1,1
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COMMENTS
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Assuming the prime k-tuples conjecture, Granville shows (in section 2.4) that this sequence is infinite.
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LINKS
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Table of n, a(n) for n=1..13.
Andrew Granville, Prime number patterns
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FORMULA
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a(n) = 2*A119751(n)+1. - Don Reble, Aug 17 2021
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EXAMPLE
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The pairwise averages of {3,7,19} are the primes {5,11,13}.
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MATHEMATICA
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s={3, 7}; i=5; Do[While[ !And@@PrimeQ[(s+Prime[i])/2], i++ ]; AppendTo[s, Prime[i]]; i++, {n, 3, 10}]; s
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CROSSREFS
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Cf. A113832, A115760, A119751.
Sequence in context: A128024 A245723 A118128 * A111974 A243100 A173400
Adjacent sequences: A113872 A113873 A113874 * A113876 A113877 A113878
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KEYWORD
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nonn,hard,more
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AUTHOR
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T. D. Noe, Jan 26 2006
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EXTENSIONS
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More terms from Don Reble and Giovanni Resta, Feb 15 2006
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STATUS
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approved
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